# How do you find the domain and range of #F(x) = -2(x + 3)² - 5#?

##### 1 Answer

Jun 30, 2018

#### Explanation:

#"this is a polynomial of degree 2 and is defined for all "#

#"real values of "x#

#"domain is "x inRR#

#"to find the range we require the vertex and if maximum"#

#"or minimum turning point"#

#"the equation of a parabola in "color(blue)"vertex form"# is.

#•color(white)(x)y=a(x-h)^2+k#

#"where "(h,k)" are the coordinates of the vertex and a"#

#"is a multiplier"#

#f(x)=-2(x+3)^2-5" is in this form"#

#"with "(h,k)=(-3,-5)" and "a=-2#

#"since " a <0" then maximum turning point"#

#"range is "y in(-oo,-5]#

graph{-2(x+3)^2-5 [-28.46, 28.5, -14.22, 14.25]}